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Boss lesson · The Flywheel Final
Exam-hall rules, one wheel
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Exam-hall rules, one wheel

This is the boss. No calculator, and one declared convention: on this paper 2π=62\pi = 6. That is a 4.5% lie, said out loud, and it is the same move as rounding gg to 10 — every line then lands on a whole number and the chain stays in your head. What is being examined here is the chain, not the fourth digit. In the real world you carry 6.283; at a whiteboard, in front of a colleague, you carry 6.

One flywheel, read end to end, and every answer feeds the next: the nameplate rpm becomes ω\omega, the disk's mass and radius become II, the two together become the energy banked, and the run-up time turns that energy into the power the drive had to find. Write each line down as you go — one slip at the top rolls all the way to the invoice.

Then one last shaft question, because the number a machine designer actually needs is never the power. 5★ under par here is the chapter crown. Clock in.

ωT

ω=2πT\omega = \frac{2\pi}{T}

  • ω\omega= Angular velocity (angular speed)
  • TT= Period (time)
Angular Velocity from Period solver →
rIm

I=12mr2I = \tfrac{1}{2} m r^{2}

  • II= Moment of inertia (moment of inertia)
  • mm= Mass (mass)
  • rr= Radius (length)
Moment of Inertia: Solid Disk solver →
IωKE

KErot=12Iω2KE_{rot} = \tfrac{1}{2} I \omega^{2}

  • KErotKE_{rot}= Rotational kinetic energy (energy)
  • II= Moment of inertia (moment of inertia)
  • ω\omega= Angular velocity (angular speed)
Rotational Kinetic Energy solver →
Pτω

P=τωP = \tau \omega

  • PP= Power (power)
  • τ\tau= Torque (torque)
  • ω\omega= Angular velocity (angular speed)
Rotational Power (P = τω) solver →
no calculator in the boss room — the numbers are chosen to fit in your head